We consider a system of mutually interacting spin 1/2 embedded in a
transverse magnetic field which undergo a second order quantum phase
transition. We analyze the entanglement properties and the spin squeezing of
the ground state and show that, contrarily to the one-dimensional case, a
cusp-like singularity appears at the critical point λc​, in the
thermodynamic limit. We also show that there exists a value λ0​≥λc​ above which the ground state is not spin squeezed despite a
nonvanishing concurrence.Comment: 4 pages, 4 EPS figures, minor corrections added and title change